Preheat the oven to 350 (while bread is having its last rising session).

• Whisk together active dry yeast, salt, sugar and warm, room temperature water in a large mixing bowl. Allow the yeast mixture to rest for 10 minutes to activate.
• Whisk oil, honey and whole wheat flour into the activated yeast mixture, then transfer the bowl to a stand mixer (you can also add flour one cup at a time and knead by hand if you wish).
• Add one cup bread flour and mix on low-medium speed until flour is well incorporated. Continue adding flour (one cup at a time) and mixing until the dough no longer sticks to the bowl and is soft and pliable. Place the dough into a lightly greased or lightly floured bowl and cover with a tea towel. Allow to rest for one hour.
• After one hour, remove the dough and shape it into 3 large balls. Roll each ball of dough out into an 8 by 8 inch circle. Cut the dough into chunks (similar to monkey bread). Add 1 egg, 1 4 oz. can green chiles and 1 cup shredded cheese per loaf. Mix the cheese, egg and green chiles into the bread dough chunks, then transfer the dough to a bread pan lined with parchment paper (this bread tends to stick to the bread pans after baking) and allow the bread to rest for another 45 minutes. *see note.
• Bake the bread on the center racks of the oven for 35-45 minutes until it is a nice, deep brown color on the top. Ensure the bread is well baked to fully cook the egg. Slather tops with butter (optional) and enjoy! Keep refrigerated.